Magnesium oxide-water compounds at megabar pressure and implications on planetary interiors

Magnesium Oxide (MgO) and water (H2O) are abundant in the interior of planets. Their properties, and in particular their interaction, significantly affect the planet interior structure and thermal evolution. Here, using crystal structure predictions and ab initio molecular dynamics simulations, we find that MgO and H2O can react again at ultrahigh pressure, although Mg(OH)2 decomposes at low pressure. The reemergent MgO-H2O compounds are: Mg2O3H2 above 400 GPa, MgO3H4 above 600 GPa, and MgO4H6 in the pressure range of 270–600 GPa. Importantly, MgO4H6 contains 57.3 wt % of water, which is a much higher water content than any reported hydrous mineral. Our results suggest that a substantial amount of water can be stored in MgO rock in the deep interiors of Earth to Neptune mass planets. Based on molecular dynamics simulations we show that these three compounds exhibit superionic behavior at the pressure-temperature conditions as in the interiors of Uranus and Neptune. Moreover, the water-rich compound MgO4H6 could be stable inside the early Earth and therefore may serve as a possible early Earth water reservoir. Our findings, in the poorly explored megabar pressure regime, provide constraints for interior and evolution models of wet planets in our solar system and beyond.

Previous study considered MgO and H2O are separated at tens of GPas. This paper challenged this concept, proposed this system to hundreds of GPas and found several meaningful compounds of Mg2O3H2, MgO4H6 and MgO3H4. Their results are rather important to the model of ice giants, such as Uranus and Neptune. In this way, I suggest it to be publish in Nat. Commun. But their papers could be improved, and my comments are as following: Phase diagram 1. Compared with Mg2O3H2 and MgO4H6, MgO3H4 seems to have a lower solid-superionic temperature and higher superionic-liquid temperature. It is an interesting phenomenon. But why? Electronic conductivity, 2. Can the authors explain why H2O has a much higher proton conductivity than MgO-H2O compounds? Thermal conductivity 3. More discussion is needed for relationship between low luminosity. Why would the planet have low luminosity if it has a heat barrier inside? Are there any related references? 4. Why MgO-H2O has lower thermal conductivity than MgO could be discussed in physics with more details. 5. Their description in method to get thermal conductivity is confused. What does i-th flux represent? Is it for ionic thermal flux or electronic thermal flux? For the planet model, 6. Why the authors believed there is a gradual transition zone between Ice and MgO-H2O layers? Based their calculation, there should be a boundary not a gradual transition zone. For In this paper, the authors combine the crystal structure prediction method with MD simulation techniques to study a set of new Mg-O-H compounds that will be thermodynamically stable at the pressure condition close to the interiors of Earth, Uranus and Neptune. They propose that the existence of such water-bearing compounds can be used to refine the evolution models of wet planets. The authors are very experienced in this area. Similar computational techniques have been applied to many other systems by the same group of authors in the recent years. Therefore, I have no technical comments on this manuscript. It can be published without major revision if the editor believe that the topic fit the scope of Nat. Comm.
That said, I have some reservation about the readership of this manuscript. The results look fancy to the general readers when people just started to employ crystal structure prediction to study the planetary minerals. However, the authors have published tens of similar works in general physics journals like Nat. Phys., Phys. Rev. series and PNAS in the past decade. To make a true impact, the authors should submit their work to more specialized journals like Astrophysics, Icarus, J. Geophys. Res., Mon. Not. R. Astron. Soc., or Nat. Astronomy.
Reviewer #3 (Remarks to the Author): The authors report a prediction of three new magnesium oxide-water compounds at megabar pressures. Magnesium and water do react to form Mg(OH)2 at condition, but the product decomposes at 27 GPa. The authors found, using multiple structure prediction methods, that magnesium and water can react again at ultrahigh pressures, specifically, Mg2O3H2 would form above 400 GPa, MgO3H4 above 700GPa, and MgO4H6 in the pressure range of 270-600 GPa. These conditions are close to the pressure conditions of the interior of several planets. Therefore, this finding suggests that water may be stored in MgO rock in the deep interiors of Earth to Neptune mass planets. I think this is a very interesting idea that is suitable for publication in Nature Communications. In particular, one of the predicted compounds, MgO4H6, is estimated to contain 57.3 wt % of water, much higher than the previously reported hydrous minerals. I have a few comments that the authors may consider.
(1) The authors features 'superionic' behaviors of the MgO-H2O compounds prominently. I am wondering whether there is a quantifiable definition of superionicity? The molecular dynamics map does show the protons are all over the place, but I do not believe we should eyeball a superionic state.
(2) What is the abundance of MgO and H2O in the interior of the planets? There must be a reasonable amount of both for the current prediction to be relevant.
(3) The predicted compounds contains a large amount of hydrogen, and therefore quantum effects are expected to be significant. Would the VASP MD and machine learning version of AIMD still be adequate to describe the behaviors of these compounds, in particular the dynamics of hydrogen? This part of simulation is perhaps more appropriate done with other methods such as path integral molecular dynamics. The authors may comment or justify their choice of method.   We thank the referee for raising this point, which made us to perform deeper analysis. We have added these discussions into the revised manuscript.

/ 13
Electronic conductivity, 2. Can the authors explain why H2O has a much higher proton conductivity than MgO-H2O compounds?
Reply: We've updated the electronic conductivity data in the manuscript. As is shown in Fig. 5. (b), in the temperature range from 1000 K to 6000 K at 600 GPa, the electrical conductivity of Mg2O3H2 is 0.36-11.07/Ωcm in Mg2O3H2, 26-93/Ωcm for MgO3H4, and Reply: Basically, the low luminosity (surface heat flux) of Uranus means that its surface is very cold. So, either all the its heat has been lost, or the heat is captured inside.
It has been hypothesized that some form of thermal boundary slows down the cooling process. A gradual composition distribution can serve as such as a heat barrier, by suppressing the heat convection. We think that the relationship between low luminosity and the heat barrier is not the major topic of our paper, so we only make a brief

Why MgO-H2O has lower thermal conductivity than MgO could be discussed in physics with more details.
Reply: At 600 GPa, MgO is solid between 3000~6000 K, while MgO-H2O compounds are superionic. In solid insulator crystals, the thermal conductivity relates to its crystal structure. The main contributor to heat transport is lattice thermal flux. In superionic phase materials, however, the ion diffusion breaks the periodic lattice, and ionic thermal flux plays the major role in heat transport. In MgO-H2O compounds, the contribution from the ionic thermal flux cannot compensate for the reduction of lattice heat flux, leading to lower thermal conductivity in MgO-H2O compounds. 6 / 13

Their description in method to get thermal conductivity is confused. What does i-th flux represent? Is it for ionic thermal flux or electronic thermal flux?
Reply: Theoretically, i-th flux represent all the flux which should be considered. In this study, since all three MgO-H2O compounds are insulator, we did not take electronic thermal flux into consideration. Another reason for us to ignore the electronic thermal flux is that we used more than 6000 atoms to run the MD simulations, making it impossible to get electron wave functions. So, in this paper i-th flux represent ionic thermal flux and the lattice thermal flux.

What κ and σ represent should be given in the title of Fig 4
Reply: The explanation of κ and σ has been added.
We appreciate all the referee's valuable comments again, which help us to improve our manuscript substantially. Soc., or Nat. Astronomy.

Reply:
We are glad that the referee knows some of our previous work. And we thank the referee for the overall positive comment on this work. We think this work and in particular the prediction of the most water-rich compound found so far, is a significant progress for exoplanet astrophysics and planetary science and will attract many general readers from different fields, such as physics, materials science, astronomy, planetary science, geochemistry, etc. Therefore, we believe Nature Communications is a proper arena for this work.
Reviewer #3 (Remarks to the Author): The authors report a prediction of three new magnesium oxide-water compounds at megabar pressures. Magnesium   In this work, we calculate the diffusion coefficients from the slope of mean squared 9 / 13 displacement (MSD): D = MSD/6t, and define the superionic regime as DH > 10 -9 m 2 /s.
(2) What is the abundance of MgO and H2O in the interior of the planets? There must be a reasonable amount of both for the current prediction to be relevant. Astron. 5, 744-745 (2021)] about planet models. As a result, we can safely assume that MgO as one of the main components of the rocky core. H2O is the most abundant ice, and the first to condense in the protoplanetary disk, thus it is expected to be main components of "hot ice" layer. We've added this part to the manuscript. Phys. Commun. 185, 1019-1026 (2014)] package, together with our machine learning force field to evaluate the nuclear quantum effects (NQEs). For comparison, we run a PIMD simulation with 16 beads and a classical MD (CMD) for MgO4H6 at 5000 K, 400 GPa. We compare their mean square displacement (MSD) and radial distribution function (RDF), as is shown in Figure R3. We find that the difference between PIMD and CMD is neglectable in this case. NQEs are often considered to be significant at relatively low temperature. Since our paper focus on the temperature condition of planetary interior (10 3~1 0 4 k), we consider NQEs can be neglected in our case. We've added this part to supplemental information.